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Activity Number: 290
Type: Contributed
Date/Time: Tuesday, August 5, 2014 : 8:30 AM to 10:20 AM
Sponsor: IMS
Abstract #312098 View Presentation
Title: Single-Index Modulated Multiple Testing
Author(s): Lilun Du*+ and Chunming Zhang
Companies: University of Wisconsin-Madison and University of Wisconsin-Madison
Keywords: Bivariate normality ; Local false discovery rate ; Multiple comparison ; p-value ; Simultaneous inference ; Symmetry property
Abstract:

In the context of large-scale multiple testing, hypotheses are often accompanied with certain prior information. In this talk, we present a single-index modulated (SIM) multiple testing procedure, which maintains control of the false discovery rate while incorporating prior information, by assuming the availability of a bivariate p-value, (p1, p2), for each hypothesis, where p1 is a preliminary p-value from prior information and p2 is the primary p-value for the ultimate analysis. To find the optimal rejection region for the bivariate p-value, we propose a criteria based on the ratio of probability density functions of (p1, p2) under the true null and non-null. This criteria in the bivariate normal setting further motivates us to project the bivariate p-value to a single-index, p(t), for a wide range of directions theta. The true null distribution of p(t) is estimated via parametric and nonparametric approaches, leading to two procedures for estimating and controlling the false discovery rate. To derive the optimal projection direction theta, we propose a new approach based on power comparison, which is further shown to be consistent under some mild conditions.


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